1. Solve Linear Systems by
Multiplying First
Section 7.4
P. 451

2. Steps
1. Arrange the equations with like terms in
columns.
2. Multiply one or both of the the equations by
a number to obtain coefficients that are
opposites for one of the variables.
3. Add /Subt the equations and one term/variable
will be eliminated. Solve for the other.
4. Substitute the value in Step 3 into either of the
original equations. Solve for other variable.
5. Check solution in each of the original
equations.

3. 6x + 5y = 19
2x + 3y = 5 Multiply by: ?

4. • Sometimes you need to use a “multiple” of
one equation to get terms eliminated. This
means multiplying each term by the same
number. (Equivalent equations)
• Solve 3x = -6y + 12 -x + 3y = 6

5. EXAMPLE 2 Multiply both equations, then subtract
Solve the linear system:
4x + 5y = 35 Equation 1
2y = 3x – 9 Equation 2
SOLUTION
STEP 1
Arrange: the equations so that like terms are in
columns.
4x + 5y = 35 Write Equation 1.
–3x + 2y = –9 Rewrite Equation 2.

6. EXAMPLE 2 Multiply both equations, then subtract
STEP 2
Multiply: Equation 1 by 2 and Equation 2 by 5 so that
the coefficient of y in each equation is the least
common multiple of 5 and 2, or 10.
4x + 5y = 35 8x + 10y = 70
–3x + 2y = –9 –15x +10y = –45
STEP 3 Subtract: the equations. 23x = 115
STEP 4 Solve: for x. x=5

7. EXAMPLE 2 Multiply both equations, then subtract
STEP 5
Substitute: 5 for x in either of the original equations
and solve for y.
4x + 5y = 35 Write Equation 1.
4(5) + 5y = 35 Substitute 5 for x.
y=3 Solve for y.
ANSWER The solution is (5, 3).

8. • Solve: 2x = 4y + 8 3y = 5x - 13

9. Do P. 454 3-12
Show original equation and then new
equation (s) through multiplication.
Show solution in ordered pair (x, y)